{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>date</th>\n",
       "      <th>time</th>\n",
       "      <th>ir</th>\n",
       "      <th>lidar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95819</td>\n",
       "      <td>305</td>\n",
       "      <td>214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95822</td>\n",
       "      <td>299</td>\n",
       "      <td>211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95826</td>\n",
       "      <td>292</td>\n",
       "      <td>199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95829</td>\n",
       "      <td>321</td>\n",
       "      <td>208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95832</td>\n",
       "      <td>298</td>\n",
       "      <td>212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95835</td>\n",
       "      <td>327</td>\n",
       "      <td>212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95838</td>\n",
       "      <td>293</td>\n",
       "      <td>215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95840</td>\n",
       "      <td>309</td>\n",
       "      <td>218</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95843</td>\n",
       "      <td>323</td>\n",
       "      <td>208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95846</td>\n",
       "      <td>292</td>\n",
       "      <td>217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95850</td>\n",
       "      <td>294</td>\n",
       "      <td>215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95852</td>\n",
       "      <td>323</td>\n",
       "      <td>218</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95856</td>\n",
       "      <td>319</td>\n",
       "      <td>218</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95858</td>\n",
       "      <td>313</td>\n",
       "      <td>214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95902</td>\n",
       "      <td>298</td>\n",
       "      <td>209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95905</td>\n",
       "      <td>296</td>\n",
       "      <td>211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95908</td>\n",
       "      <td>294</td>\n",
       "      <td>210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95911</td>\n",
       "      <td>314</td>\n",
       "      <td>215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95914</td>\n",
       "      <td>300</td>\n",
       "      <td>212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95917</td>\n",
       "      <td>324</td>\n",
       "      <td>219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95920</td>\n",
       "      <td>295</td>\n",
       "      <td>220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95922</td>\n",
       "      <td>320</td>\n",
       "      <td>214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95925</td>\n",
       "      <td>302</td>\n",
       "      <td>211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95928</td>\n",
       "      <td>303</td>\n",
       "      <td>215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95932</td>\n",
       "      <td>297</td>\n",
       "      <td>215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95934</td>\n",
       "      <td>306</td>\n",
       "      <td>210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95937</td>\n",
       "      <td>302</td>\n",
       "      <td>217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95940</td>\n",
       "      <td>296</td>\n",
       "      <td>215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95943</td>\n",
       "      <td>308</td>\n",
       "      <td>213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>20180122</td>\n",
       "      <td>95947</td>\n",
       "      <td>303</td>\n",
       "      <td>211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58958</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115907</td>\n",
       "      <td>297</td>\n",
       "      <td>210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58959</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115910</td>\n",
       "      <td>320</td>\n",
       "      <td>204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58960</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115914</td>\n",
       "      <td>324</td>\n",
       "      <td>205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58961</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115917</td>\n",
       "      <td>302</td>\n",
       "      <td>199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58962</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115919</td>\n",
       "      <td>299</td>\n",
       "      <td>203</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58963</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115923</td>\n",
       "      <td>298</td>\n",
       "      <td>206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58964</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115925</td>\n",
       "      <td>301</td>\n",
       "      <td>206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58965</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115929</td>\n",
       "      <td>321</td>\n",
       "      <td>206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58966</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115932</td>\n",
       "      <td>319</td>\n",
       "      <td>209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58967</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115935</td>\n",
       "      <td>311</td>\n",
       "      <td>208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58968</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115938</td>\n",
       "      <td>326</td>\n",
       "      <td>204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58969</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115941</td>\n",
       "      <td>319</td>\n",
       "      <td>206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58970</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115944</td>\n",
       "      <td>303</td>\n",
       "      <td>201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58971</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115947</td>\n",
       "      <td>323</td>\n",
       "      <td>203</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58972</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115950</td>\n",
       "      <td>302</td>\n",
       "      <td>205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58973</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115953</td>\n",
       "      <td>314</td>\n",
       "      <td>202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58974</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115956</td>\n",
       "      <td>326</td>\n",
       "      <td>204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58975</th>\n",
       "      <td>20180124</td>\n",
       "      <td>115959</td>\n",
       "      <td>308</td>\n",
       "      <td>201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58976</th>\n",
       "      <td>20180124</td>\n",
       "      <td>120002</td>\n",
       "      <td>302</td>\n",
       "      <td>209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58977</th>\n",
       "      <td>20180124</td>\n",
       "      <td>120005</td>\n",
       "      <td>303</td>\n",
       "      <td>207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58978</th>\n",
       "      <td>20180124</td>\n",
       "      <td>120009</td>\n",
       "      <td>310</td>\n",
       "      <td>206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58979</th>\n",
       "      <td>20180124</td>\n",
       "      <td>120012</td>\n",
       "      <td>330</td>\n",
       "      <td>208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58980</th>\n",
       "      <td>20180124</td>\n",
       "      <td>120015</td>\n",
       "      <td>305</td>\n",
       "      <td>205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58981</th>\n",
       "      <td>20180124</td>\n",
       "      <td>120018</td>\n",
       "      <td>301</td>\n",
       "      <td>202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58982</th>\n",
       "      <td>20180124</td>\n",
       "      <td>120021</td>\n",
       "      <td>320</td>\n",
       "      <td>206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58983</th>\n",
       "      <td>20180124</td>\n",
       "      <td>120023</td>\n",
       "      <td>313</td>\n",
       "      <td>208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58984</th>\n",
       "      <td>20180124</td>\n",
       "      <td>120026</td>\n",
       "      <td>297</td>\n",
       "      <td>200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58985</th>\n",
       "      <td>20180124</td>\n",
       "      <td>120030</td>\n",
       "      <td>323</td>\n",
       "      <td>204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58986</th>\n",
       "      <td>20180124</td>\n",
       "      <td>120033</td>\n",
       "      <td>326</td>\n",
       "      <td>207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58987</th>\n",
       "      <td>20180124</td>\n",
       "      <td>120036</td>\n",
       "      <td>321</td>\n",
       "      <td>208</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>58988 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           date    time   ir  lidar\n",
       "0      20180122   95819  305    214\n",
       "1      20180122   95822  299    211\n",
       "2      20180122   95826  292    199\n",
       "3      20180122   95829  321    208\n",
       "4      20180122   95832  298    212\n",
       "5      20180122   95835  327    212\n",
       "6      20180122   95838  293    215\n",
       "7      20180122   95840  309    218\n",
       "8      20180122   95843  323    208\n",
       "9      20180122   95846  292    217\n",
       "10     20180122   95850  294    215\n",
       "11     20180122   95852  323    218\n",
       "12     20180122   95856  319    218\n",
       "13     20180122   95858  313    214\n",
       "14     20180122   95902  298    209\n",
       "15     20180122   95905  296    211\n",
       "16     20180122   95908  294    210\n",
       "17     20180122   95911  314    215\n",
       "18     20180122   95914  300    212\n",
       "19     20180122   95917  324    219\n",
       "20     20180122   95920  295    220\n",
       "21     20180122   95922  320    214\n",
       "22     20180122   95925  302    211\n",
       "23     20180122   95928  303    215\n",
       "24     20180122   95932  297    215\n",
       "25     20180122   95934  306    210\n",
       "26     20180122   95937  302    217\n",
       "27     20180122   95940  296    215\n",
       "28     20180122   95943  308    213\n",
       "29     20180122   95947  303    211\n",
       "...         ...     ...  ...    ...\n",
       "58958  20180124  115907  297    210\n",
       "58959  20180124  115910  320    204\n",
       "58960  20180124  115914  324    205\n",
       "58961  20180124  115917  302    199\n",
       "58962  20180124  115919  299    203\n",
       "58963  20180124  115923  298    206\n",
       "58964  20180124  115925  301    206\n",
       "58965  20180124  115929  321    206\n",
       "58966  20180124  115932  319    209\n",
       "58967  20180124  115935  311    208\n",
       "58968  20180124  115938  326    204\n",
       "58969  20180124  115941  319    206\n",
       "58970  20180124  115944  303    201\n",
       "58971  20180124  115947  323    203\n",
       "58972  20180124  115950  302    205\n",
       "58973  20180124  115953  314    202\n",
       "58974  20180124  115956  326    204\n",
       "58975  20180124  115959  308    201\n",
       "58976  20180124  120002  302    209\n",
       "58977  20180124  120005  303    207\n",
       "58978  20180124  120009  310    206\n",
       "58979  20180124  120012  330    208\n",
       "58980  20180124  120015  305    205\n",
       "58981  20180124  120018  301    202\n",
       "58982  20180124  120021  320    206\n",
       "58983  20180124  120023  313    208\n",
       "58984  20180124  120026  297    200\n",
       "58985  20180124  120030  323    204\n",
       "58986  20180124  120033  326    207\n",
       "58987  20180124  120036  321    208\n",
       "\n",
       "[58988 rows x 4 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd    ###dataread###（1〜4行目と出力の上5行くらいを図示）\n",
    "data  = pd.read_csv(\"sensor_data_200.txt\", delimiter=\" \", \n",
    "                    header=None, names = (\"date\",\"time\",\"ir\",\"lidar\"))\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0    214\n",
      "1    211\n",
      "2    199\n",
      "3    208\n",
      "4    212\n",
      "Name: lidar, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "print(data[\"lidar\"][0:5]) ###getvalues###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xPSIerX+PrPGIiI9HxExE3BcRJzY051REPNO2TP9mGDk7ZD23bv8iIibnPOayWqaPRMQZTcw5qvfpIjn/PiK+Ve/DL0bEEW2PGfryXErWBi7TyyvjPRHx1Yj49Rrv/XOfmX7VF/CHwInAA21jdwJ/VNPvBS6v6VXt8w0557HAiTX9K8C3geOBvwMurfFLgStr+izgK0AApwK3NzTnFPDlhi3T36V1Psw0MNk2//HAvcChwGrgO8BBDcw5kvfpIjlPBw6u8SvbfvYjWZ5LzNq0ZfqKtnn+Arimpnv+3LuG0CYzvw7snTP8GuDrNb0dePtQQ80jM/dk5jdr+sfAw7TOAl8HbK3ZtgLn1PQ64LpsuQ04IiKObWDOkVkoa2Y+nJnznRy5DrghM5/NzO8CM7QuzdK0nCOxSM6vZuZszXYbrXORYETLc4lZR2KRnD9qm+1wYP+O4Z4/9xZCZw/SWrAA5/L8E+tWR8TdEfGfEfEHw4/WWn0FTgBuByYyc0/d9X1goqbnu2TIiiFFBLrOCfCGiLg3Ir4SEa8dZsb95mRdSNOW6WJG+j5dJOd7af0GCw1YntB1VmjYMo2IKyLiceB8YP+m1p6XqYXQ2XuBP4+Iu2itpv1vje8BfiMzTwD+EvjXqP0LwxIRLwc+D7xvzm8JZGudsRGHkPWQ85u0Trl/HfCPwL8NNSiLZ22SHnKO9H26UM6I+CAwC1w/rCyd9JC1ccs0Mz+YmSsr48WLPX4xFkIHmfmtzDw9M08CPkNr2ya1avtUTd9V468ZVq6IOITWm+L6zPxCDT+xf5Ww/n2yxjteMqQJOTPzR5m5r6ZvBg6JiKOHkXORrAtp2jKd1yjfpwvljIgLgLcC59cvBDDC5VmZus7axGXa5np+uVm752VqIXQQEb9a/74E+Gvgmrp9TLT+vgMR8VvAGuCxIWUK4Frg4cz8aNtd24D1Nb0euKlt/N111MGpwDNtm2wakzMifq0eQ0ScTOv9+dSgc3bIupBtwHkRcWhErKb1879jkBmh95yjep8ulDNafyDr/cDbMvOnbQ8ZyfJcStYGLtM1bbOtA75V071/7pe6x/vF+EVrDWAP8H+0trddCFxCa2/+t4FN/PJkvrfT2r9wD61NHX88xJy/T2szy331/e+hdUTBq4BbgUeB/wCOqvmD1h8m+g5wP21HoTQs58W1TO+ltRPv9xqwTP+k3gvPAk8At7Q95oO1TB8B3tLEnKN6ny6Sc4bWdu39Y9eMcnkuJWsDl+nngQdq/Eu0djQv6XPvmcqSJMBNRpKkYiFIkgALQZJULARJEmAhSJKKhSBJAiwESVKxECRJAPw/GE/2+Whus9sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "data[\"lidar\"].hist(bins = max(data[\"lidar\"]) - min(data[\"lidar\"]),align='left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "209.73713297619855 209.73713297619855\n"
     ]
    }
   ],
   "source": [
    "mean1 = sum(data[\"lidar\"].values)/len(data[\"lidar\"].values)   ###calcmean###\n",
    "mean2 = data[\"lidar\"].mean()\n",
    "print(mean1,mean2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data[\"lidar\"].hist(bins = max(data[\"lidar\"]) - min(data[\"lidar\"]),color=\"orange\",align='left')   ###avgplot###\n",
    "plt.vlines(mean1,ymin=0,ymax=5000,color=\"red\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23.407709770274106\n",
      "23.40810659855441\n",
      "23.4077097702742\n",
      "23.408106598554504\n",
      "23.4077097702742\n",
      "23.408106598554504\n"
     ]
    }
   ],
   "source": [
    "# 定義から計算　                     ### calcvar\n",
    "zs = data[\"lidar\"].values  \n",
    "mean = sum(zs)/len(zs)\n",
    "diff_square = [ (z - mean)**2 for z in zs]\n",
    "\n",
    "sampling_var = sum(diff_square)/(len(zs))     # 標本分散\n",
    "unbiased_var = sum(diff_square)/(len(zs)-1) # 不偏分散\n",
    "\n",
    "print(sampling_var)\n",
    "print(unbiased_var)\n",
    "\n",
    "# Pandasを使用\n",
    "pandas_sampling_var = data[\"lidar\"].var(ddof=False) # 標本分散\n",
    "pandas_default_var = data[\"lidar\"].var()        # デフォルト（不偏分散）\n",
    "\n",
    "print(pandas_sampling_var)\n",
    "print(pandas_default_var)\n",
    "\n",
    "# NumPyを使用\n",
    "import numpy as np\n",
    "\n",
    "numpy_default_var = np.var(data[\"lidar\"])  # デフォルト（標本分散）\n",
    "numpy_unbiased_var = np.var(data[\"lidar\"], ddof=1)  # 不偏分散\n",
    "\n",
    "print(numpy_default_var)\n",
    "print(numpy_unbiased_var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.838151482774605\n",
      "4.83819249292072\n",
      "4.838192492920729\n"
     ]
    }
   ],
   "source": [
    "import math ###  calcstddev\n",
    "\n",
    "# 定義から計算\n",
    "stddev1 = math.sqrt(sampling_var)\n",
    "stddev2 = math.sqrt(unbiased_var)\n",
    "\n",
    "# Pandasを使用 \n",
    "pandas_stddev = data[\"lidar\"].std()\n",
    "\n",
    "print(stddev1)\n",
    "print(stddev2)\n",
    "print(pandas_stddev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>211</th>\n",
       "      <th>210</th>\n",
       "      <th>208</th>\n",
       "      <th>209</th>\n",
       "      <th>212</th>\n",
       "      <th>207</th>\n",
       "      <th>213</th>\n",
       "      <th>206</th>\n",
       "      <th>214</th>\n",
       "      <th>205</th>\n",
       "      <th>...</th>\n",
       "      <th>197</th>\n",
       "      <th>196</th>\n",
       "      <th>223</th>\n",
       "      <th>224</th>\n",
       "      <th>226</th>\n",
       "      <th>195</th>\n",
       "      <th>194</th>\n",
       "      <th>193</th>\n",
       "      <th>227</th>\n",
       "      <th>229</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lidar</th>\n",
       "      <td>4409</td>\n",
       "      <td>4355</td>\n",
       "      <td>4261</td>\n",
       "      <td>4228</td>\n",
       "      <td>4201</td>\n",
       "      <td>3920</td>\n",
       "      <td>3897</td>\n",
       "      <td>3674</td>\n",
       "      <td>3572</td>\n",
       "      <td>3225</td>\n",
       "      <td>...</td>\n",
       "      <td>84</td>\n",
       "      <td>59</td>\n",
       "      <td>55</td>\n",
       "      <td>32</td>\n",
       "      <td>15</td>\n",
       "      <td>13</td>\n",
       "      <td>10</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1 rows × 35 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        211   210   208   209   212   207   213   206   214   205 ...   197  \\\n",
       "lidar  4409  4355  4261  4228  4201  3920  3897  3674  3572  3225 ...    84   \n",
       "\n",
       "       196  223  224  226  195  194  193  227  229  \n",
       "lidar   59   55   32   15   13   10    4    3    1  \n",
       "\n",
       "[1 rows x 35 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freqs = pd.DataFrame(data[\"lidar\"].value_counts())  ###freqs###\n",
    "freqs.transpose() #横向きに出力してみましょう"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>211</th>\n",
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       "      <th>208</th>\n",
       "      <th>209</th>\n",
       "      <th>212</th>\n",
       "      <th>207</th>\n",
       "      <th>213</th>\n",
       "      <th>206</th>\n",
       "      <th>214</th>\n",
       "      <th>205</th>\n",
       "      <th>...</th>\n",
       "      <th>197</th>\n",
       "      <th>196</th>\n",
       "      <th>223</th>\n",
       "      <th>224</th>\n",
       "      <th>226</th>\n",
       "      <th>195</th>\n",
       "      <th>194</th>\n",
       "      <th>193</th>\n",
       "      <th>227</th>\n",
       "      <th>229</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lidar</th>\n",
       "      <td>4409.000000</td>\n",
       "      <td>4355.000000</td>\n",
       "      <td>4261.000000</td>\n",
       "      <td>4228.000000</td>\n",
       "      <td>4201.000000</td>\n",
       "      <td>3920.000000</td>\n",
       "      <td>3897.000000</td>\n",
       "      <td>3674.000000</td>\n",
       "      <td>3572.000000</td>\n",
       "      <td>3225.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>84.000000</td>\n",
       "      <td>59.000</td>\n",
       "      <td>55.000000</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>13.00000</td>\n",
       "      <td>10.00000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>probs</th>\n",
       "      <td>0.074744</td>\n",
       "      <td>0.073829</td>\n",
       "      <td>0.072235</td>\n",
       "      <td>0.071676</td>\n",
       "      <td>0.071218</td>\n",
       "      <td>0.066454</td>\n",
       "      <td>0.066064</td>\n",
       "      <td>0.062284</td>\n",
       "      <td>0.060555</td>\n",
       "      <td>0.054672</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001424</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.000932</td>\n",
       "      <td>0.000542</td>\n",
       "      <td>0.000254</td>\n",
       "      <td>0.00022</td>\n",
       "      <td>0.00017</td>\n",
       "      <td>0.000068</td>\n",
       "      <td>0.000051</td>\n",
       "      <td>0.000017</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 35 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               211          210          208          209          212  \\\n",
       "lidar  4409.000000  4355.000000  4261.000000  4228.000000  4201.000000   \n",
       "probs     0.074744     0.073829     0.072235     0.071676     0.071218   \n",
       "\n",
       "               207          213          206          214          205  \\\n",
       "lidar  3920.000000  3897.000000  3674.000000  3572.000000  3225.000000   \n",
       "probs     0.066454     0.066064     0.062284     0.060555     0.054672   \n",
       "\n",
       "         ...           197     196        223        224        226       195  \\\n",
       "lidar    ...     84.000000  59.000  55.000000  32.000000  15.000000  13.00000   \n",
       "probs    ...      0.001424   0.001   0.000932   0.000542   0.000254   0.00022   \n",
       "\n",
       "            194       193       227       229  \n",
       "lidar  10.00000  4.000000  3.000000  1.000000  \n",
       "probs   0.00017  0.000068  0.000051  0.000017  \n",
       "\n",
       "[2 rows x 35 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freqs[\"probs\"] = freqs[\"lidar\"]/len(data[\"lidar\"]) ###addprobs###\n",
    "freqs.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(freqs[\"probs\"])  ###confirmsum###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "freqs[\"probs\"].sort_index().plot.bar(color=\"blue\")   ###probdist###\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "210"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def drawing(): #ややこしいので関数として定義  ###one_sampling###\n",
    "    return freqs.sample(n=1, weights=\"probs\").index[0]\n",
    "\n",
    "drawing() # 実行"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples = [ drawing() for i in range(len(data))] ### sampling_simulation ###\n",
    "#samples = [ drawing() for i in range(100)] #コーディング中は1行目の代わりにこちらを使う\n",
    "simulated = pd.DataFrame(samples, columns=[\"lidar\"])\n",
    "p = simulated[\"lidar\"]\n",
    "p.hist(bins = max(p) - min(p),color=\"orange\",align='left')  \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def p(z, mu=209.7, dev=23.4):   ###pdf_from_def###\n",
    "    return math.exp(-(z - mu)**2/(2*dev))/math.sqrt(2*math.pi*dev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "zs = range(190,230)   ###pdf_plot_from_def###\n",
    "ys = [p(z) for z in zs]\n",
    "\n",
    "plt.plot(zs,ys)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def prob(z,width=0.5):                                     ###prob_plot_from_def###\n",
    "    return width*( p(z-width) + p(z+width) )\n",
    "\n",
    "zs = range(190,230)\n",
    "ys = [prob(z) for z in zs]\n",
    "\n",
    "plt.bar(zs,ys, color=\"red\", alpha=0.3) #alphaでグラフを透明にできる\n",
    "f = freqs[\"probs\"].sort_index()\n",
    "plt.bar(f.index, f.values, color=\"blue\", alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm    ###pdf_plot_from_lib###\n",
    "\n",
    "zs = range(190,230)\n",
    "ys = [norm.pdf(z, mean1, stddev1) for z in zs]\n",
    "\n",
    "plt.plot(zs,ys)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "zs = range(190,230)                                ###cdf###\n",
    "ys = [norm.cdf(z, mean1, stddev1) for z in zs]\n",
    "\n",
    "plt.plot(zs,ys, color=\"red\") \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "zs = range(190,230)              ###prob_cdf###\n",
    "ys = [norm.cdf(z+0.5, mean1, stddev1) -  norm.cdf(z-0.5, mean1, stddev1) for z in zs]\n",
    "\n",
    "plt.bar(zs,ys)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data[\"ir\"].hist(bins = max(data[\"ir\"]) - min(data[\"ir\"]),align='left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.ir.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
